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Positive quadrant dependence testing and constrained copula estimation. (English. French summary) Zbl 1273.62125

Summary: Positive quadrant dependence is a specific dependence structure that is of practical importance in for example modelling dependencies in insurance and actuarial sciences. This dependence structure imposes a constraint on the copula function. The interest in this paper is to test for positive quadrant dependence. One way to assess the distribution of the test statistics under the null hypothesis of positive quadrant dependence is to resample from a constrained copula. This requires constrained estimation of a copula function. We show that this use of resampling under a constrained copula improves considerably the power performance of existing testing procedures.
We propose two resampling procedures, one based on a parametric constrained copula estimation and one relying on nonparametric estimation of a positive quadrant dependence copula, and discuss their properties. The finite-sample performances of the resulting testing procedures are evaluated via a simulation study that also includes comparisons with existing tests. Finally, a data set of Danish fire insurance claims is tested for positive quadrant dependence.

MSC:

62H15 Hypothesis testing in multivariate analysis
62G09 Nonparametric statistical resampling methods
62H20 Measures of association (correlation, canonical correlation, etc.)
65C60 Computational problems in statistics (MSC2010)
62G05 Nonparametric estimation

Software:

copula; copula; R
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References:

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